Quantum superposition

superpositionsuperpositionscoherent superpositionmixSuperposedadmixturealive and dead simultaneouslylinear combinationsprinciple of superpositionquantum bit
Quantum superposition is a fundamental principle of quantum mechanics.wikipedia
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Schrödinger equation

Schrödinger's equationwave mechanicsSchrödinger wave equation
Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution.
The superposition property allows the particle to be in a quantum superposition of two or more quantum states at the same time.

Superposition principle

superpositionlinear superpositionsuperpose
It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states.
A primary approach to computing the behavior of a wave function is to write it as a superposition (called "quantum superposition") of (possibly infinitely many) other wave functions of a certain type—stationary states whose behavior is particularly simple.

Quantum entanglement

entanglemententangledentangled state
For quantum amplitudes, the word entanglement replaces the word correlation, but the analogy is exact.
The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum necessarily has more than one term.

Bra–ket notation

Dirac notationketBra-ket notation
Here |0 \rangle is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement.
.)*Quantum superpositions can be described as vector sums of the constituent states.

Quantum mechanics

quantum physicsquantum mechanicalquantum theory
Quantum superposition is a fundamental principle of quantum mechanics.
All of the possible consistent states of the measured system and the measuring apparatus (including the observer) are present in a real physical – not just formally mathematical, as in other interpretations – quantum superposition.

Path integral formulation

path integralFeynman path integralpath integrals
The analogous expression in quantum mechanics is the path integral.
In quantum mechanics, the state is a superposition of different states with different values of q, or different values of p, and the quantities p and q can be interpreted as noncommuting operators.

Schrödinger's cat

Schrödinger catSchrodinger's CatSchrödinger’s Cat
In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted this dissonance between quantum mechanics and classical physics.
The scenario presents a hypothetical cat that may be simultaneously both alive and dead, a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur.

Quantum computing

quantum computerquantum computationquantum computers
In quantum computing the phrase "cat state" often refers to the GHZ state, the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1; i.e.,
Whereas traditional models of computing such as the Turing machine or Lambda calculus rely on "classical" representations of computational memory, a quantum computation could transform the memory into a quantum superposition of possible classical states.

Quantum state

eigenstatepure stateeigenstates
Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states.
Nevertheless, such factors are important when state vectors are added together to form a superposition.

Qubit

qubitsquantum bitquantum bits
In quantum computing the phrase "cat state" often refers to the GHZ state, the special entanglement of qubits wherein the qubits are in an equal superposition of all being 0 and all being 1; i.e., Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" |0 \rangle and |1 \rangle.
However, quantum mechanics allows the qubit to be in a coherent superposition of both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing.

Density matrix

density operatordensity matricesvon Neumann equation
The mechanism that achieves this is a subject of significant research, one mechanism suggests that the state of the cat is entangled with the state of its environment (for instance, the molecules in the atmosphere surrounding it), when averaged over the possible quantum states of the environment (a physically reasonable procedure unless the quantum state of the environment can be controlled or measured precisely) the resulting mixed quantum state for the cat is very close to a classical probabilistic state where the cat has some definite probability to be dead or alive, just as a classical observer would expect in this situation.
A mixed state is different from a quantum superposition.

Penrose interpretation

PenrosePenrose interpretation of quantum mechanicsPenrose's objective-collapse theory
Penrose proposes that a quantum state remains in superposition until the difference of space-time curvature attains a significant level.

Quantum decoherence

decoherencedecoheredecohered
One modern view is that this mystery is explained by quantum decoherence.
As a consequence, the system behaves as a classical statistical ensemble of the different elements rather than as a single coherent quantum superposition of them.

Linearity

linearlinearlycomplex linear
Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution. The fundamental law of quantum mechanics is that the evolution is linear, meaning that if state A turns into A′ and B turns into B′ after 10 seconds, then after 10 seconds the superposition \psi turns into a mixture of A′ and B′ with the same coefficients as A and B.

Wave interference

interferenceconstructive interferencedestructive interference
An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment.

Electron

electronse − electron mass
An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment.

Diffraction

diffraction patterndiffractdiffracted
The pattern is very similar to the one obtained by diffraction of classical waves.

Quantum information science

quantum information processingquantum communicationquantum informatics
Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" |0 \rangle and |1 \rangle.

Bit

bitsbinary digitbinary digits
Contrary to a classical bit that can only be in the state corresponding to 0 or the state corresponding to 1, a qubit may be in a superposition of both states.

Complex number

complexreal partimaginary part
The principle of quantum superposition states that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number.

Paul Dirac

DiracPaul Adrien Maurice DiracP. A. M. Dirac
The principle was described by Paul Dirac as follows:

Anton Zeilinger

ZeilingerA. ZeilingerProf. Anton Zeilinger
Anton Zeilinger, referring to the prototypical example of the double-slit experiment, has elaborated regarding the creation and destruction of quantum superposition:

Linear equation

linearlinear equationsslope-intercept form
each solve the linear equation on ψ, then

Coefficient

coefficientsleading coefficientfactor
The fundamental law of quantum mechanics is that the evolution is linear, meaning that if state A turns into A′ and B turns into B′ after 10 seconds, then after 10 seconds the superposition \psi turns into a mixture of A′ and B′ with the same coefficients as A and B.

Wave function

wavefunctionwave functionsnormalized
The quantity \psi(x) is called the wavefunction of the particle.